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These NCERT Solutions for Class 8 Science Chapter 10 Reaching the Age of Adolescence Questions and Answers are prepared by our highly skilled subject experts to help students while preparing for their exams.

Reaching the Age of Adolescence NCERT Solutions for Class 8 Science Chapter 10

Class 8 Science Chapter 10 Reaching the Age of Adolescence Textbook Exercise Questions and Answers

Page 124-125

Question 1.
What is the term used for chemical secretions of endocrine glands responsible for changes taking place in the body?
Answer:
The chemical substances secreted by the endocrine glands are called hormones.
Hormones are responsible for the various changes taking place in the body.

Question 2.
Define adolescence.
Answer:
The period of life when many changes are taking place in the body leading to reproductive maturity, is called adolescence. It begins around the age of 11 years and lasts upto 18 or 19 years.

Question 3.
What is menstruation? Explain.
Answer:
In females, one egg is released by either of the ovaries each month. After that, the uterine walls develop a thickening to support the foetus and prepare for a possible pregnancy. If fertilisation does not take place, the egg and the thickening of uterus walls are discarded in small fragments. This results in bleeding through the vagina for some days. The bleeding (through vagina) at the end of menstrual cycle is called menstruation.

Question 4.
List changes in the body that take place at puberty.
Answer:
Following changes take place in the body at the time of puberty:

• Sudden increase in height and weight.
• Broadening of shoulders and widening of chest in boys. In girls, the region below waist becomes wider.
• In boys, under the influence of hormones, the larynx becomes prominent and the vocal cords become longer and thicker. These changes make the voice hoarse.
• Appearance of hair in underarms, face, hands, legs and pubic region.
• Appearance of acne as a result of excessive secretion of oil glands in the skin.
• Testes grow and start producing sperms in males, whereas in females, the ovary enlarges and starts producing mature eggs.

Question 5.
Prepare a table having two columns depicting names of endocrine glands and hormones secreted by them.
Answer:
The table below shows endocrine glands and the hormones secreted by them:

Question 6.
What are sex hormones? Why are they named so? State their function.
Answer:
Hormones which influence the functions of gonads and facilitate the appearance of secondary sexual characters are called sex hormones. Testosterone and estrogen are the main sex hormones.
i. Testosterone: In males, the testes produce the male sex hormone called testosterone. This hormone helps in the development and maintenance of the primary and secondary sexual characters such as growth of beard, development of reproductive organs, production of sperms, etc.

ii. Estrogen: In females, the ovaries secrete estrogen and progesterone which are responsible for the development of primary and secondary sexual characters such as the enlargement of breasts, development of female reproductive organs, etc.

Question 7.
Choose the correct option:
a. Adolescents should be careful about what they eat, because
i. proper diet develops their brains
ii. proper diet is needed for the rapid growth taking place in their body
iii. adolescents feel hungry all the time
iv. taste buds are well developed in teenagers
Answer:
(ii) proper diet is needed for the rapid growth taking place in their body.

b. Reproductive age in women starts when their
i. menstruation starts
ii. breasts start developing
iii. body weight increases
iv. height increases
Answer:
(i) menstruation starts

c. The right meal for adolescents consists of
i. chips, noodles, coke
ii. chapati, dal, vegetables
iii. rice, noodles and burger
iv. vegetable cutlets, chips and lemon drink
Answer:
(ii) chapati, dal, vegetables

Question 8.
Write notes on-
a. Adam’s apple
b. Secondary sexual characters
c. Sex determination in the unborn baby
Answer:
a. Adam’s apple: At puberty, the voice box or the larynx begins to grow. Boys develop larger voice boxes. The increase in the size of voice box in boys is seen as a prominence in the neck. This protrusion is called Adam’ apple.

b. Secondary sexual characters: These are the characters which distinguish a male from a female are called secondary sexual characters. Some examples are given below:

• In males, the growth of hair is seen on face and body.
• Hair growth in the pubic region, under the arms, etc., is seen in both males and females.
• In boys, voice becomes deeper.
• Increase in weight.
• Shoulders become broad and chest gets widened in males. The hips become wider in females.
• The development of breasts takes place in females.
• Mood swings are seen in males as well as females. Mental and emotional maturity is attained by both the sexes. Brain becomes active and has a larger capability of learning.

c. Sex determination in the unborn baby: Gametes in humans have 23 chromosomes, i.e., half the total number of chromosomes in somatic cells. So, a sperm may have an X or a Y chromosome as 23rd chromosome. But, an ovum has only X chromosome as 23rd chromosome. If a sperm with X chromosome fertilises the egg, the zygote thus formed will lead to the birth of a girl child. If a sperm with Y chromosome fertilises the egg, the zygote thus formed will lead to – the birth of a male child.

Question 9.
Word game: Use the clues to work out the words.
Across
3. Protruding voice box in boys
4. Glands without ducts
7. Endocrine gland attached to brain
8. Secretion of endocrine glands
9. Pancreatic hormone
10. Female hormone

Down
1. Male hormone
2. Secretes thyroxine
3. Another term for teenage
5. Hormone reaches here through bloodstream
6. Voice box
7. Term for changes at adolescence

Answer:
Across
3. Adam’s apple
4. Endocrine
7. Pituitary
8. Hormone
9. Insulin
10. Estrogen

Down
1. Testosterone
2. Thyroid
3. Adolescence
5. Target site
6. Larynx
7. Puberty

Question 10.
The table below shows the data on likely heights of boys and girls as they grow in age. Draw graphs showing height and age for both boys and girls on the same graph paper. What conclusions can be drawn from these graphs?

Answer:

We conclude that initially, girls grow faster than boys but, by about 18 years of age both reach their maximum height. Boys are, in general, taller than girls. The rate of growth in height varies in different individuals.

NCERT Extended Learning Activities and Projects

Question 1.
Find out from your elder relatives about their awareness of the legal status of early marriage. You yourself may get information on it from your teacher, parents, a doctor or the internet. Write a two-minute speech explaining why early marriage is not good for the couple.
Hint:
Early marriage has a great impact on the body of a woman. Early marriages lead to early pregnancies and because of these pregnancies the life of a girl suffers danger. Marriage needs lots of commitment, understanding and the capability to shoulder numerous responsibilities which cannot be expected from two very young people. Maturity is something that is directly related to age. It may vary from person to person but there’s no doubt that a young couple will have a sense of immaturity. Moreover, getting married in early age means that the couples do not even have financial stability which leads to the collapse of such family. In addition, this also creates obstruction for their studies. Hence, early marriages are not good at all.

Question 2.
Collect newspaper cuttings and information in magazines about HIV/ AIDS. Write a one page article of 15 to 20 sentences on HIV/AIDS.
Hint:
HIV stands for Human Immunodeficiency Virus. It harms the immune system by destroying the white blood cells that fight infection. This puts a person at risk of serious infections and certain cancers. AIDS stands for Acquired Immunodeficiency Syndrome. It is the final stage of infection with HIV. Not everyone with HIV develops AIDS. HIV most often spreads through unprotected sex with an infected person. It may also spread by sharing drug needles or through contact with the blood of an infected person. Women can give it to their babies during pregnancy or childbirth. The first signs of HIV infection may be swollen glands and flu-like symptoms. These may come and go within two to four weeks. Severe symptoms may not appear until months or years. A blood test can tell if you have an HIV infection. Your health care provider can do the test, or you can use a home testing kit. There is no cure, but there are many medicines that fight HIV infection and lower the risk of infecting others. People who get early treatment can live with the disease for a longer time.

Question 3.
In our country, according to 2011 census, there are 940 adolescent females for every 1000 males. Find out
a. the concerns of the community regarding this low ratio. Remember that the chance of having a boy or a girl is equal.
b. what amniocentesis is and how useful this technique is. Why is its use for identification of sex of the unborn child banned in India?
Hint:
a. The concerns of the community regarding the low ratio are as follows:

• Social imbalance: The decrease in sex ratio would result in social imbalance. In a society the number of male and female should be equal because unequal number would result in social imbalance.
• Marriage squeeze: With the declining number of sex ratio, the institution of marriage would be worst affected because there will be no girl for marriage.
• Immoral trafficking: As the sex ratio plunges down, people would resort to immoral trafficking where girls would be sold and bought for marriage. Their status would be degraded.
• Sexual offences against women would rise with decline in sex ratio. There would also be a rise in sexually transmitted diseases.

b. Amniocentesis is a diagnostic test usually done during pregnancy. This test involves removing small amount of amniotic fluid (the fluid surrounding a developing foetus) from the uterus. The amniotic fluid can be tested to determine if the fetus has certain kinds of birth defects.

Usage of this test is banned because of illegal practice of using it to determine the sex of the child and killing the unborn girl child (female infanticide).

Question 4.
Put your ideas together and write a short note on the importance of knowing facts about reproduction.
Hint:
By knowing the facts about reproduction, humans can either plan to have children or avoid unwanted pregnancies. It helps to remove social superstitions and be better aware of ourselves. It can also reduce the chances and spread of sexually transmitted diseases. It also helps to maintain hygiene and health. Hence, it is important.

Activity 1

Objective: To study and compare the gain in height of boys and girls at different ages.
Procedure: Use the data given below to draw a graph. Take age on the X-axis and present growth in height on the Y-axis. Highlight the point representing your age on the graph. Find out the percentage of height you have already reached. Calculate the height you might eventually reach.

Observation:

Suppose your present height is 120 cm and the point of your age is 14 years which touches the 93% mark on height axis.
So,
Full height = \(\frac{\text { Present height }(\mathrm{cm})}{\% \text { of full height at this age }}\) × 100
= \(\frac{120 \mathrm{~cm}}{93}\) × 100
= 129 cm
Hence, the height you may eventually reach is 129 cm.

Conclusion: It is evident from the graph that initially, girls grow faster than boys but by about 18 years of age, both reach their maximum height.

Secondary Sexual Characters: Characters which help in distinguishing a male from a female are called secondary sexual characters. The marked difference between the males and females of a species because of apparent physical traits is called sexual dimorphism.

• Secondary sexual characters in boys: Facial hair, deep voice and hair on chest.
• Secondary sexual characters in girls: Enlargement of breasts and high-pitched voice.
• Some common characters in girls and boys: Hair under armpits and in pubic region.

Hormones: Hormones are the chemical substances secreted by the endocrine glands for proper functioning and controlled changes taking place during adolescence in the human body. Endocrine glands are also known as ductless glands. These glands release hormones directly into the bloodstream to reach a particular body part known as the target site.

• In boys, testes secrete the hormone testosterone. This hormone is responsible for the secondary sexual characters in males, like growth of facial hair, etc.
• In girls, the ovaries secrete the hormone estrogen. This is responsible for the secondary sexual characters in females, e.g., development of breasts, etc.

Hormonal control: The production of sex hormones (testosterone from testes and estrogen from ovaries) is under the control of another hormone secreted from an endocrine gland called pituitary gland. The pituitary secretes many hormones, one of which stimulates the maturation of ova in the ovaries and sperms in the testes.

Reproductive Phase of Life in Humans: The reproductive phase begins with the onset of puberty and it happens at around the same age in boys and girls. But reproductive phase in men lasts much longer than in females. Reproductive phase in women lasts till about 50 years of age, while in men it lasts even beyond 60 years of age.
i. Menstruation: In females, one egg is released by either of the ovaries every month. After that, the uterus develops a thickening to support a foetus to prepare for a possible pregnancy. If fertilisation does not take place, the egg and the thickening in uterus walls are discarded in small fragments. This results in bleeding through the vagina for some days. The bleeding (through vagina) at the end of menstrual cycle is called menstruation.

ii. Menstrual Cycle: The cycle of events which begins from the maturation and release of an egg and ends with shedding off of the uterine lining along with the egg is called menstrual cycle. A menstrual cycle is usually of 28 to 30 days.

iii. Menarche: The first menstrual bleeding in a woman’s life is called menarche. Menarche marks the beginning of puberty in girls.

iv. Menopause: Cessation of menstrual cycle is called menopause. This happens at around 45-50 years of age. Menopause marks the end of reproductive phase in females.

Sex determination: Gender of a child is determined by the combination of chromosomes in the zygote. A normal human cell has 46 chromosomes, i.e., 23 pairs of chromosomes. Out of them, 22 pairs of chromosomes are identical. But chromosomes in the 23rd pair may be identical or different.

There are two types of chromosomes in 23rd pair. They are called X and Y chromosomes (together called sex chromosomes). The 23rd pair in a male has XY combination, while in a female it has XX combination.

Gametes in humans have 23 chromosomes, i. e., half the total number of chromosomes in usual body cells. So, a sperm may have an X or a Y chromosome as 23rd chromosome. But, an ovum always has an X chromosome as 23rd chromosome.
i. If a sperm with X chromosome fertilises the egg, the zygote thus formed will have an XX combination and will lead to the birth of a girl child.
ii. If a sperm with Y chromosome fertilises the egg, the zygote thus formed will have an XY combination and will lead to the birth of a male child.

harmones other than sex Harmones:

Role of Hormones in Completing the Life Cycle of Insects and Frogs: Insect hormones control the metamorphosis of larva into adult. Thyroxine hormone controls the metamorphosis of tadpole larva into frog. If a frog lays eggs in iodine deficient water, the tadpoles will not develop into frogs and will perish.

Activity 2

Objective: To study the importance of consuming iodised salt.
Procedure: Collect information from magazines or from doctors and prepare a note on the importance of consuming iodised salt. You can also look for this information on the internet.

Observation: Iodised salt is important for the proper functioning of thyroid gland. This gland produces a hormone called thyroxine which regulates protein, fat and carbohydrate metabolism in the body. Under Secretion of this hormone causes cretinism in children (which leads to feeble mindedness) and goitre in adults (in which neck becomes swollen). Iodine is required for the production of this hormone. Hence, consuming iodised salt with food improves metabolism.

Reproductive Health:
i. Balanced Diet: Rapid growth during adolescence necessitates balanced diet which contains all the nutrients in adequate amount. A teenager should take sufficient amount of carbohydrates, proteins, fats, vitamins and minerals in food. One should avoid eating fried food and junk food. Girls need to take a lot of iron-rich food because iron is necessary for the formation of RBCs in blood.

ii. Personal Hygiene: You have read that sweat and sebaceous glands show increased activity during this period. If proper hygiene is not maintained, it can lead to many skin diseases in adolescents. Girls need to take special care of hygiene during menstrual period.

iii. Physical Exercise: Physical exercise is helpful not only in making a strong body but also in properly utilising the energy. A good workout ensures that all your systems are working in perfect condition.

iv. Say ‘NO’ to Drugs: The menace of drugs is spoiling many lives. During adolescence, one can easily get influenced and carried away by negative stimulations. You need to have a strong will power to say ‘No’ to drugs. Drugs are addictive and they harm the body in the long run. They ruin health and happiness.

v. HIV (Human Immunodeficiency Virus): This is a virus which causes AIDS (Acquired Immunodeficiency Syndrome). Till date, there is no cure for this disease. Hence, prevention is the only way to keep away from this dangerous disease. AIDS can spread through sexual contact, through infected needles and from a mother to her unborn child. This can also be transmitted to an infant through mother’s milk.

Class 8 Science Chapter 10 Reaching the Age of Adolescence Additional Important Questions and Answers

Very Short Answer Type Questions

Question 1.
What is puberty?
Answer:
The process of changes taking place in the body during adolescence to attain reproductive maturity is called puberty.

Question 2.
What indicates that a child is becoming an adult?
Answer:
The changes taking place in the body indicate that a child is becoming an adult.

Question 3.
How many pairs of chromosomes are found in the nuclei of the usual cells of human both’?
Answer:
23 pairs.

Question 4.
Name the disease caused by the lack of thyroxine hormone.
Answer:
Goitre.

Question 5.
Name the primary sex organs of human male and female.
Answer:
Testes in mates and ovaries in females.

Question 6.
At what age does the growth in human body become noticeable?
Answer:
After crossing the age of 10 or 11 years, a sudden spurt in the growth of human body becomes noticeable.

Question 7.
Is mother responsible for the sex determination of the baby?
Answer:
No, father is responsible for the sex determination of the baby as being heterogametic.

Question 8.
Do boys and girls undergo same physical changes during adolescence?
Answer:
The boys and girls undergo different physical changes during adolescence because of sexual dimorphism in humans.

Question 9.
What are the common secondary sexual characters in boys and girls of teenage?
Answer:
Hair under armpits, hair in pubic region.

Question 10.
Which gland is known as the master gland?
Answer:
Pituitary gland.

Question 11.
Which gland is responsible for the fatness in the body?
Answer:
Thyroid gland.

Question 12.
Which hormone causes sweating under fear?
Answer:
Adrenalin.

Question 13.
Do all the eggs carry similar set of chromosomes?
Answer:
Yes, all eggs carry the X chromosome.

Question 14.
What are twins?
Answer:
Twins are two offsprings produced by the same pregnancy. These can be identical or non-identical.

Short Answer Type Questions

Question 1.
What is sex chromosome? Explain briefly.
Answer:
The 23rd pair of chromosome in humans is called sex chromosome. It is of two types, i.e., X chromosome and Y chromosome. While XX combination in the 23rd pair results in the birth of a girl child, XY combination leads to the birth of a male child. Since these chromosomes are responsible for the determination of sex of the child, they are called sex chromosomes.

Question 2.
What is target site?
Answer:
Endocrine glands release hormones into the bloodstream to reach a particular body part which is called the target site. It is the site of body where the hormone produces its effects.

Question 3.
Explain in brief the development of sex organs in males and females.
Answer:
At puberty, male sex organs like testes and penis develop completely. The testes also begin to produce sperms. In girls, the ovaries enlarge and eggs begin to mature. Ovaries also start releasing mature eggs every month.

Question 4.
Write a short note on goitre.
Answer:
Goitre is a metabolic disease which happens due to iodine deficiency in the body. Iodine deficiency results in less production of thyroxine. This may result in goitre which is manifested by a permanent swelling in the neck.

Question 5.
Explain the cause of changes taking place in human body during puberty?
Answer:
There is a pituitary gland present in the body which controls the production of the hormones in both males and females. The hormones are the chemical substances released in the blood by endocrine glands like ovaries, testes or pituitary gland. The hormones secreted by pituitary stimulate testes and ovaries to secrete the male and female hormones, respectively. These hormones are responsible for the changes taking place in human body during puberty.

Question 6.
How can young boys and girls take care of their personal hygiene?
Answer:

• Everyone should take a bath daily because increased activity of sweat and oil glands makes the body unclean and prone to microbial growth.
• Girls should take special care of cleanliness during the time of menstrual flow.

Question 7.
Write the name and function of one male and one female sex hormone.
Answer:

• Male sex hormone is testosterone which is produced by testes. It produces secondary sexual characters in males and supports the production of sperms.
• Female sex hormone is estrogen which is produced by ovaries. It produces secondary sexual characters in females and supports the maturation of eggs.

Question 8.
Explain the role of hormones in completing the life cycle of frogs and insects.
Answer:
The life cycle of insects involves four different stages, namely, egg, larva, pupa and adult. The process of conversion of larva into adult through drastic changes is called metamorphosis. In insects, metamorphosis is controlled by insect hormones in the same way as is controlled by thyroxine hormone in frogs. Tadpole becomes a frog under the action of thyroxine hormone produced by thyroid. Since the production of thyroxine requires iodine, the tadpoles cannot become adults if they grew in iodine-deficient water.

Question 9.
What kind of secondary sexual characters are developed in males?
Answer:
The features in male are development of beard and moustaches. There is facial hair growth and development of deep voice. Shoulders become broad and height is increased.

Question 10.
What are the secondary sexual characters in females?
Answer:
There is a development of mammary glands or milk producing glands, development of a shrill voice, starting of menstrual cycle and widening of pelvic area.

Question 11.
What is the relation between adolescence and puberty?
Answer:
Adolescence is the period of life when a body undergoes changes leading to reproductive maturity. These changes mark the onset of puberty. Hence, adolescence is the period of life which witnesses puberty.

Question 12.
Write a short note on changes in body shape during puberty.
Answer:
There is change in body shape during puberty which includes broader shoulders and wider chests in boys and in girls, the region below the waist becomes wider.

Question 13.
How are general growth and sexual maturation different from each other?
Answer:
General growth refers to different types of developmental processes in the body like increase in height, weight gain, changes in shape and size of the body, etc. However, sexual maturation is specific to the changes reflected at puberty, like cracking of voice, new hair patterns, development of breast in females, etc.

Question 14.
The onset of puberty is controlled by hormones. Justify this statement.
Answer:
Hormones from pituitary gland stimulate the testes and ovaries to release testosterone in males and estrogen in females respectively these hormones are released in the bloodstream and reach their target sites, that is, the particular body parts where they have to show their effects. The target sites respond to the hormone and stimulate the changes in the body at onset of puberty. Thus, we can say that the onset of puberty is controlled by hormones.

Question 15.
Explain the function of pituitary gland.
Answer:
The production of all hormones is under the control of pituitary gland. The pituitary gland is termed as the ‘Master Gland’ because it directs other organs and endocrine glands, such as the adrenal glands and thyroid glands, to suppress or induce hormone production. It involves the following functions:

• Growth hormone production
• Production of hormones that act on other endocrine glands
• Production of hormones that act on the muscles and the kidneys
• Regulation of functions of endocrine glands.
• Storage of hormones produced by the hypothalamus

Long Answer Type Questions

Question 1.
Explain the menstruation and menopause.
Answer:
In girls, with the onset of puberty, the ovaries start releasing mature eggs. Either of the two ovaries produce one mature ovum after every four weeks. The process by which a mature ovum is released from an ovary is called ovulation. During this period, the wall of the uterus becomes thick. This is a natural preparation to receive the fertilised egg, in case fertilisation occurs.

If fertilisation does not occur, the released egg, and the thickened lining of the uterus along with its blood vessels are shed off. This causes bleeding called menstrual flow, and the process is called menstruation. The menstrual flow lasts for 2-7 days. Menstruation occurs once in about 28-30 days. At 45 to 50 years of age, the menstruation cycle stops. The stoppage of menstrual cycle and other associated events in the body of a female is called menopause.

Question 2.
Describe the sex determination of a baby in humans.
Answer:
We know that there are 23 pairs of chromosomes present inside the nucleus of every human cell. These chromosomes have a thread-like structure and they always occur in pairs. Out of the 23 pairs of chromosomes, the last pair is of sex chromosomes. X and Y are the two sex chromosomes. Females have two X chromosomes and males have one X and one Y chromosome. The gametes contain only one set of chromosomes (23 chromosomes), that is, either an X or a Y chromosome. The egg of the female always contains an X chromosome. However, the sperm may contain either of the X and Y chromosomes. So, if the sperm that contains a Y chromosome fertilises the egg, the zygote develops into a male. On the other hand, if the sperm that contains an X chromosome fertilises the egg, the zygote develops into a female. Hence, the sex of the child depends upon the chromosomes of the father and not the mother.

Question 3.
What should be done to maintain the physical and mental health of adolescents?
Answer:
During adolescence, there is rapid mental and physical growth. Therefore, taking care of physical and mental health at this stage is of utmost importance.
For proper physical health, one needs:

a. A balanced diet: An adolescent should consume a balanced diet containing the right amount of proteins, carbohydrates, fats, vitamins and minerals. The diet should contain adequate amount of cereals for carbohydrates; meat, milk, nuts and pulses for proteins; controlled amounts of butter/ghee/ oils and sugars for energy; and fruits and vegetables for protection against diseases. Fast food which is tasty but does not have adequate nutrition, such as chips or aerated drinks, should not be used as substitute for meals.

b. Personal hygiene: Due to increased activity of sweat and sebaceous glands, proper personal hygiene is very important for adolescents. Taking a bath every day and cleaning all parts of the body is essential, otherwise body odour and bacterial infection may occur. Girls should be specially careful about hygiene during menstruation.

c. Physical exercise: Walking, jogging, aerobics, outdoor games, etc., are good for the growing adolescent body.

Question 4.
Make a chart of various endocrine glands, their hormones and one function of each gland.
Answer:

Picture-Based Questions

Question 1.
Observe the diagram given below and answer the following questions:

a. Name the glands labelled A, B, C and D.
b. Name the hormones produced by each of the glands E and F.
c. What is the function of the gland labelled D.
Answer:
a. A – Pituitary gland
B – Thyroid gland
C – Adrenal gland
D – Pancreas

b. E – Estrogen
F – Testosterone

c. D is pancreas which releases insulin. Insulin maintains the blood sugar levels.

Question 2.
Observe the figure and answer the following questions:

a. Name the part shown here.
b. Is it present in males or in females?
Answer:
a. Adam’s apple.
b. Males.

These NCERT Solutions for Class 9 Maths Chapter 10 Circles Ex 10.1 Questions and Answers are prepared by our highly skilled subject experts.

NCERT Solutions for Class 9 Maths Chapter 10 Circles Exercise 10.1

Question 1.
Fill in the blanks:
(i) The centre of a circle lies in ________ of the circle. (exterior/interior)
(ii) A point, whose distance from the centre of a circle is greater than its radius lies in _______ of the circle. (exterior/interior)
(iii) The longest chord of a circle is a ________ of the circle.
(iv) An arc is a ________ when its ends are the ends of a diameter.
(v) Segment of a circle is the region between an arc and _________ of the circle.
(vi) A circle divides the plane on which it lies, in ________ parts.
Solution:
(i) Interior
(ii) Exterior
(iii) Diameter
(iv) Semicircle
(v) The chord
(vi) Three

Question 2.
Write True or False: Give reasons for your answer.
(i) Line segment joining the centre to any point on the circle is a radius of the circle.
(ii) A circle has only a finite number of equal chords.
(iii) If a circle is divided into three equal arcs each is a major arc.
(iv) A chord of a circle, which is twice as long as its radius is the diameter of the circle.
(v) Sector is the region between the chord and its corresponding arc.
(vi) A circle is a plane figure.
Solution:
(i) True
(ii) False, A circle has an infinite number of equal chords.
(iii) False, if a circle is divided into three equal arcs then each is a minor area.
(iv) True
(v) False, sector is the region between the radius and corresponding arc.
(vi) True.

These NCERT Solutions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles Ex 9.4 Questions and Answers are prepared by our highly skilled subject experts.

NCERT Solutions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles Exercise 9.4

Question 1.
Parallelogram ABCD and rectangle ABEF are on the same base AB and have equal areas. Show that the perimeter of the parallelogram is greater than that of the rectangle.
Solution:
Given: Parallelogram ABCD and rectangle ABEF with the same base AB and equal areas.

To prove that: Perimeter of ||gm ABCD > perimeter of rectangle ABEF.
i.e., AB + BC + CD + AD > AB + BE + EF + AF.
Proof: Since opposite sides of a ||gm and a rectangle are equal.
∴ AB = CD (Opposite sides of || gm)
and AB = EF (Opposit sides of rectangle)
∴ CD = EF
or AB + CD = AB + EF ……(i)
Now, we know that all the segments tlat can be drawn to a given line from a point not lying on it, the perpendicular segment is the shortest.
∴ BE < BC and AF < AD
∴ BC + AD > BE + AF ……(ii)
Adding (i) and (ii) we get
AB + CD + BC + AD > AB + EF + BE + AF
or, AB + BC + CD + AD > AB + BE + EF + AF
Therefore, the perimeter of || gm ABCD > perimeter of rectangle ABEF.

Question 2.
In Fig. 9.30, D and E are two points on BC such that BD = DE = EC. Show that ar (ABD) = ar (ADE) = ar (AEC). Can you now answer the question that you have left in the ‘Introduction’, of this chapter, whether the Held of Budhia has been actually divided into three parts of equal area?

Solution:
Given: In ΔABC, D and E are two points on BC such that BD = DE = EC.
To prove that: ar (ΔABD) = ar (ΔADE) = ar (ΔAEC)
Construction: Draw AL ⊥ BC
Proof: In ΔADE
ar (ΔADE) = \(\frac {1}{2}\) × DE × AL ……(i)
ar (ΔABD) = \(\frac {1}{2}\) × BD × AL
or, ar (ΔABD) = \(\frac {1}{2}\) × DE × AL …(ii) (∵ BD = DE)
From equation (i) and (ii)
ar (ΔADE) = ar (ΔABD) …..(iii)
Again, ar (ΔAEC) = \(\frac {1}{2}\) × EC × AL
or, ar (ΔAEC) = \(\frac {1}{2}\) × DE × AL ……(iv) (∵ EC = DE given)
From equation (i) and (iv)
ar (ΔADE) = ar (ΔAEC) …..(v)
From equation (iii) and (v)
ar (ΔABD) = ar (ΔADE) = ar (ΔAEC)
Yes, Budhiya has used the result of this question in dividing her land into three equal parts.

Question 3.
In Fig. 9.31, ABCD, DCFE, and ABFE are parallelograms. Show that ar (ADE) = ar (BCF).

Solution:
In ΔADE and ΔBCF
AD = BC (Opposite sides of || gm ABCD)
DE = CF (Opposite sides of || gm DCFE)
and AE = BF (Opposite sides of || gm ABFE)
By S-S-S congruency condition.
ΔADE ≅ ΔBCF
We know that two congruent triangles have equal areas.
Therefore, ar (ΔADE) = ar (ΔBCF)

Question 4.
In Fig. 9.32, ABCD is a parallelogram, and BC is produced to a point Q such that AD = CQ. If AQ intersects DC at P, show that ar (BPC) = ar (DPQ).

Solution:
Given: ABCD is a parallelogram in which side BC is produced to Q such that AD = CQ.
To prove that: ar (ΔBPC) = ar (ΔDPQ)
Construction: Join AC which intersects BP at O.
Proof: ΔBPC and ΔAPC lie on the same base PC and between the same parallel lines AB and CD.
∴ ar (ΔBPC) = ar (ΔAPC) ……(i)
(Δs on the same base and between same parallels are equal in the area)
Again, ΔCQD and ΔACQ lie on the same base CQ and between the same parallel lines AD and BQ.
∴ (ΔCQD) = ar (ΔACQ) …….(ii)
(As on the same base and between same parallels are equal in the area)
or, ar (ΔCQD) – ar (ΔCQP) = ar (ΔACQ) – ar (ΔCQP)
(Subtract ar (ΔCQP) both side)
ar (ΔDPQ) = ar (ΔAPC) ……(iii)
From equation (i) and (iii),
ar (ΔBPC) = ar (ΔDPQ)

Question 5.
In Fig. 9.33, ABC and BDE are two equilateral triangles such that D is the midpoint of BC. If AE intersects BC at F, show that
(i) ar (BDE) = \(\frac {1}{4}\) ar (ABO)
(ii) ar (BDE) = \(\frac {1}{2}\) ar (BAE)
(iii) ar (ABC) = 2ar (BEC)
(iv) ar (BFE) = ar (AFD)
(v) ar (BFE) = 2ar (FED)
(vi) ar (FED) = \(\frac {1}{8}\) ar (AFC)

Solution:
Given: ABC and BED are two equilateral triangles. D is the midpoints of BC, and AE intersects BC at F.
To prove that:
(i) ar (BDE) = \(\frac {1}{4}\) ar (ABO)
(ii) ar (BDE) = \(\frac {1}{2}\) ar (BAE)
(iii) ar (ABC) = 2ar (BEC)
(iv) ar (BFE) = ar (AFD)
(v) ar (BFE) = 2ar (FED)
(vi) ar (FED) = \(\frac {1}{8}\) ar (AFC)

Construction: Join CE and AD and draw EG ⊥ BC and join.
Proof: ΔABC and ΔDEF both equilateral Δs.
∴ ∠ABC = ∠BDE (each 60°)
But it is the pair of alternate interior angle and we know that if pair of alternate interior angles are equal then the two lines are parallel.
∴ AB || DE
Similarly, AC || BE and AD || EF
(i) ar (ΔBDE) = \(\frac{\sqrt{3}}{4}\) (BD)²
(∵ Area of equilateral Δ = \(\frac{\sqrt{3}}{4}\) a²)
= \(\frac{\sqrt{3}}{4}\left(\frac{1}{2} \mathrm{BC}\right)^{2}\) (∵ D is mid point of BC)
\(\frac{\sqrt{3}}{4} \times \frac{1}{4} \mathrm{BC}^{2}\)
= \(\frac {1}{4}\) ar (ΔABC)
(∵ Area of equilateral Δ = \(\frac{\sqrt{3}}{4}\) a²)
So, ar (ΔBDE) = \(\frac {1}{4}\) ar (ΔABC)

(ii) ar(ΔBDE)= \(\frac {1}{2}\) ar(ΔBEC)
(∵ ED is the median of ΔEBC and median divide a Δ into two equal parts)
ΔBEC and ΔBAE lie on same base BE and between same parallels BE and AC.
∴ ar (ΔBEC) = ar (ΔBAE) ……(b)
(Δs on same base and between same parallels are equal in area)
From equation (a) and (b)
ar (ΔBDE) = \(\frac {1}{2}\) ar (ΔBAE)

(iii) We have
ar (ΔBEC) = ar (ΔBAE) ……(i)
(Prove above equ. (b))
Now, ΔBAE and ΔBAD lie on same base BA and between same parallels AB and DE.
∴ ar (ΔBAE) = ar (ΔBAD) ……(ii)
But ar (ΔBAD) = \(\frac {1}{2}\) ar (ΔABC) ……(iii)
(∵ median divides a triangle into two equal parts)
From equation (i), (ii) and (iii)
ar (ΔBEC) = \(\frac {1}{2}\) ar (ΔABC)
or, ar (ΔABC) = 2 ar (ΔBEC)

(iv) ΔBDE and ΔADE lie on same base DE and between same parallels DE and AB.
∴ ar (ΔBDE) = ar (ΔADE)
or, ar (ΔBDE) – ar (ΔDEF) = ar (ΔADE) – ar (ΔDEF)
[Subtract ar (ΔDEF) both side]
or, ar (ΔBFE) = ar (ΔAFD)

(v) In ΔABC and ΔDEB

Again, ΔDEB and ΔDEA lie on same base DE and between same parallels DE and AB.
∴ ar (ΔDEB) = ar (ΔDEA)
or, ar (ΔDEB) – ar (ΔDEA) = ar (ΔDEA) – ar (ΔDEF)
(Subtract ar (ΔDEF) both side)
or, ar (ΔBEF) = ar (ΔADF) ……(b)

(vi) We have given that
BC = 2BD = 2 (BF + FD) (∵ BD = BF + FD)
= 2 (2FD + FD) [From equation (c), BF = 2DF]
or, BC = 6FD ……(d)

Question 6.
Diagonals AC and BD of a quadrilateral ABCD intersect each other at P. Show that: ar (APB) × ar (CPD) = ar (APD) × ar (BPC)
Solution:
Given: ABCD is a quadrilateral in which diagonal, AC, and BD intersect each other at P.
To prove that: ar (APB) × ar (CPD) = ar (APD) × ar(BPC)

Construction: Draw, AM ⊥ BD, and CN ⊥ BD.
Proof: ar (ΔAPB) × ar (ΔCPD) = \(\frac {1}{2}\) × PB × AM × \(\frac {1}{2}\) × PD × CN
= \(\frac {1}{2}\) × PB × CN × \(\frac {1}{2}\) × PD × AM
= ar (ΔBPC) × ar (ΔAPD)
∴ ar (ΔAPB) × ar (ΔCPD) = ar (ΔAPD) × ar (ΔBPC)

Question 7.
P and Q are respectively the midpoints of sides AB and BC of a triangle ABC and R is the midpoint of AP. Show that
(i) ar (PRQ) = \(\frac {1}{2}\) ar (ARC)
(ii) ar (RQC) = \(\frac {3}{8}\) ar(ABC)
(iii) ar (PBQ) = ar (ARC)

Solution:
Given: P and Q are the midpoint of the side AB and BC respectively and R is the midpoint of AP.
To prove that:
(i) ar (PRQ) = \(\frac {1}{2}\) ar (ARC)
(ii) ar (RQC) = \(\frac {3}{8}\) ar(ABC)
(iii) ar (PBQ) = ar (ARC)
Construction: Join AQ, CP, CR and PQ.
Proof: (i) In ΔAPC,
R is the mid point of AP.
So, ar (ΔARC) = ar (ΔPRC)
(Median divide a triangle into two equal parts)
or, ar (ΔARC) = \(\frac {1}{2}\) ar (ΔAPC) ……(i)
Now, ar (ΔAPC) = \(\frac {1}{2}\) ar (ΔABC) ……(ii)
(PC is the median of ΔABC)
and ar (ΔAQB) = \(\frac {1}{2}\) ar (ΔABC) ……(iii)
(∵ AQ is the median of ΔABC)
From equation (i) and (ii) we get
ar (ΔAPC) = ar (ΔAQB) ……(A)
From equation (ii) and (iii) we get
ar (ΔAPC) = ar (ΔAQB) …..(iv)
Again, ar (ΔAPQ) = \(\frac {1}{2}\) ar (ΔABQ) ……(v)
(∵ PQ is the median of ΔAQB)
ar (ΔPRQ) = \(\frac {1}{2}\) ar (ΔAPQ)
(∵ QR is the median ΔAQP)
or, ar (ΔPRQ) = \(\frac {1}{2}\) × \(\frac {1}{2}\) ar (ΔABQ) (∵ from equation (v))
= \(\frac {1}{4}\) ar (ΔAQB) (∵ from equation (A))
or, ar (ΔPRQ) = \(\frac {1}{4}\) . 2 ar (ΔARC)
(∵ ar ΔARC = \(\frac {1}{2}\) ar (ΔAPC))
or, ar (ΔPRQ) = \(\frac {1}{2}\) ar (ΔARC)

(ii) In ΔRBC, RQ is the median.
∴ ar (ΔRBQ) = ar (ΔRCQ) …….(I)
(median divide a Δ into tqo equal parts)
But, ar (ΔRBQ) = ar (ΔAQB) – ar (ΔAQR)
= \(\frac {1}{2}\) ar (ΔABC) – \(\frac {1}{8}\) ar (ΔABC)
(∵ ar (ΔAQB) = \(\frac {1}{2}\) ar (ΔABC) and ar(ΔAQR) = \(\frac {1}{8}\) ar (ΔABC))
ar (ΔRBQ) = \(\frac {3}{8}\) ar (ΔABC) ……..(II)
From equation I and II we can say.
ar (ΔRQC) = \(\frac {3}{8}\) ar (ΔABC)

(iii) In ΔABQ, QP is the median
ar (ΔPBQ) = \(\frac {1}{2}\) ar (ΔABQ)
(∵ QP is the median)
= \(\frac {1}{2}\) × \(\frac {1}{2}\) ar (ΔABC)
(∵ ar (ΔABQ) = \(\frac {1}{2}\) ar (ΔABC))
or, ar(ΔPBQ) = \(\frac {1}{4}\) ar(ΔABC) ……(a)
Again, ar (ΔARC) = \(\frac {1}{4}\) ar (ΔACP)
(∵ CR is the median of ΔACP)
= \(\frac {1}{2}\) × \(\frac {1}{2}\) ar (ΔABC)
(∵ ar (ΔACP) = \(\frac {1}{2}\) ar (ΔABC))
or, ar (ΔARC) = \(\frac {1}{4}\) ar (ΔABC) ……(b)
From equation (a) and (b) we get
ar (ΔPBQ) = ar (ΔARC).

Question 8.
In Fig. 9.34, ABC is a right triangle right angled at A. BCFD, ACFG and ABMN are squares on the sides BC, CA, and And AB respectively. Line AX ⊥ DE meets BC at Y. Show that:
(i) ΔMBC ≅ ΔABD
(ii) ar (BYXD) = 2 ar (MBC)
(iii) ar (BYXD) = ar (ABMN)
(iv) ΔFCB ≅ ΔACE
(v) ar (CYXE) = 2 ar (FCB)
(vi) ar (CYXE) = ar (ACFG)
(vii) ar (BCED) = ar (ABMN) + ar (ACFG)

Solution:
(i) In ΔMBC and ΔABD
MB = AB (Sides of square ABMN)
BC = BD (Sides of square BCED)
∠MBA = ∠CBD (each 90°)
or, ∠MBA + ∠ABC = ∠CBD + ∠ABC
or, ∠MBC = ∠ABD
So, By S-A-S congruency condition
ΔMBC ≅ ΔABD …….(i)

(ii) BYXD and ΔABD lie on the same base BD and between the same parallels BD and AX.
∴ ar (BYXD) = 2 ar (ΔABD)
[If a rectangle and a triangle lie on the same base and between same || is then the area of Δ is half of the rectangle]
or, a (DBYXD) = 2 ar (ΔMBC) [from (i) congruent Δ is have equal area]

(iii) We have
ar (BYXD) = 2 ar (ΔMBC) ……(ii)
(Prove above)
and ar (ABMN) = 2 ar (OMBC) …….(iii)
(Because they lie on same base BM and between same || lines MB and NC]
From equation (ii) and (iii)
ar (BYXD) = ar (ABMN)

(iv) In ΔFCB and ΔACE
FC = AC (Sides of square)
CB = CE (Sides of square)
∠FCA = ∠BCE (each 90°)
∠FCA + ∠ACB = ∠BCE + ∠ACB (Add ∠ACB both side)
or, ∠FCB = ∠ACE
So, by S-A-S Congruency Condition
ΔFCB = ΔACE …….(iv)

(v) CYXE and ΔACE lie on samp base CE and between the same parallels CE and AX.
(∵ ar (CYXE) = 2ar (ΔACE))
(If a rectangle and a Δ lie on the same base and between same || lines then ar if the rectangle is double the area of Δ)
or, ar (CYXE) = 2 ar (∠FCB)
(From equ. (iv) congruent Δ have equal area)

(vi) ACFG and ΔFCB lie on same base CF and between same parallels CF and BG.
∴ ar (ACFG) = 2ar (ΔFCB) …….(vi)
From equation (v) and (vi)
ar (CYXE) = ar (ACFG)

(vii) ΔABC, is a right angle triangle right angled at A.
∴ By pythagorus theorem,
BC² = AB² + AC²
or, ar (Square BCED) = ar (Square ABMN) + ar (Square ACFG) [∵ Area of square = (side)²]
ar(BCED) = ar(ABMN) + ar(ACFG).

These NCERT Solutions for Class 6 Maths Chapter 10 Mensuration Ex 10.2 Questions and Answers are prepared by our highly skilled subject experts.

NCERT Solutions for Class 6 Maths Chapter 10 Mensuration Exercise 10.2

Question 1.
Find the areas of the following figures by counting square:


Answer:
(a) Number of filled square = 9
∴ Area covered by squares = 9 × 1 = 9 sq. units

(b) Number of filled squares = 5
∴ Area covered by filled squares = 5 × 1 = 5 sq. units

(c) Number of full filled squares = 2
Number of half-filled squares = 4
∴ Area covered by full filled squares = 2 × 1 = 2 sq. units
And Area covered by half-filled squares = 4 × \(\frac { 1 }{ 2 }\) = 2 sq. units
∴ Total area = 2 + 2 = 4 sq. units

(d) Number of filled squares = 8
∴ Area covered by filled squares = 8 × 1 = 8 sq. units

(e) Number of filled squares = 10
∴ Area covered by filled squares = 10 × 1 = 10 sq. units

(f) Number of full filled squares = 2
Number of half-filled squares = 4
∴ Area covered by full filled squares = 2 × 1 = 2 sq. units
And Area covered by half-filled squares = 4 × \(\frac { 1 }{ 2 }\) = 2 sq. units
∴ Total area = 2 + 2 = 4 sq. units

(g) Number of full filled squares = 4
Number of half-filled squares = 4
∴ Area covered by full filled squares = 4 × 1 = 4 sq. units
And Area covered by half-fille squares = 4 × \(\frac { 1 }{ 2 }\) = 2 sq. units
∴ Total area = 4 + 2 = 6 sq. units

(h) Number of filled squares = 5
∴ Area covered by filled squares = 5 × 1 = 5 sq. units

(i) Number of filled squares = 9
∴ Area covered by filled squares = 9 × 1 = 9 sq. units

(j) Number of full filled squares = 2
Number of half-filled squares = 4
∴ Area covered by full filled squares = 2 × 1 = 2 sq. units
And Area covered by half-fille squares = 4 × \(\frac { 1 }{ 2 }\) = 2 sq. units
∴ Total area = 2 + 2 = 4 sq. units

(k) Number of full filled squares = 4
Number of half-filled squares = 2
∴ Area covered by full filled squares = 4 × 1 = 4 sq. units
And Area covered by half-filled squares = 2 × \(\frac { 1 }{ 2 }\) = 1 sq. units
∴ Total area = 4 + 1 = 5 sq. units

(l) Number of full filled squares = 3
Number of half-filled squares = 10
∴ Area covered by full filled squares = 3 × 1 = 3 sq. units
And Area covered by half-filled squares = 10 × \(\frac { 1 }{ 2 }\) = 5 sq. units
∴ Total area = 3 + 5 = 8 sq. units

(m) Number of full filled squares = 7
Number of half-filled squares = 14
∴ Area covered by full filled squares = 7 × 1 = 7 sq. units
And Area covered by half-filled squares = 14 × \(\frac { 1 }{ 2 }\) = 7 sq. units
∴ Total area = 7 + 7 = 14 sq. units

(n) Number of full filled squares = 10 Number of half-filled squares = 16
∴ Area covered by full filled squares = 10 × 1 = 10 sq. units
And Area covered by half-filled squares = 16 × \(\frac { 1 }{ 2 }\) = 8 sq. units
∴ Total area = 10 + 8 = 18 sq. units

These NCERT Solutions for Class 6 Maths Chapter 7 Fractions Ex 7.1 Questions and Answers are prepared by our highly skilled subject experts.

NCERT Solutions for Class 6 Maths Chapter 7 Fractions Exercise 7.1

Question 1.
Write the fraction representing the shaded portion.

Answer:

Question 2.
Colour the part according to the given fraction.
Answer:

Question 3.

Identify the error if any.
Answer:
The given figures do not represent the correct fractions as the part are unequal.

Question 4.
What fraction of a day is 8 hours?
Answer:
We know that in a day there are 24 hours.
So, 8 hours in a 24-hours day is represented as \(\frac{8}{24}=\frac{1}{3}\)

Question 5.
What fraction of an hour is 40 minutes?
Answer:
We know that in an hour there are 60
minutes. So, 40 minutes in a 60 min is
represented as \(\frac{40}{60}=\frac{2}{3}\)

Question 6.
Arya, Abhimanyu, and Vivek shared lunch. Arya has brought two sandwiches, one made of vegetable and one of jam. The other two boys forgot to bring their lunch. Arya agreed to share his sandwiches so that each person will have an equal share of each sandwich.
(a) How can Arya divide his sandwiches so that each person has an equal share?
(b) What part of a sandwich will each boy receive?
Answer:
(a) Since there are three people to eat, Arya should divide his sandwiches into 3 equal parts and give 1 part of each sandwich so that each person has an equal share.
(b) Each boy will receive \(\frac{1}{3}\) of a sandwich.

Question 7.
Kanchan dyes dresses. She had to dye 30 dresses. She has so far finished 20 dresses. What fraction of dresses has she finished?
Answer:
Kanchan has finished 20 dresses out of 30.
So Fraction would be \(\frac{20}{30}=\frac{2}{3}\)

Question 8.
Write the natural numbers from 2 to 12. What fraction of them are prime numbers?
Answer:
Natural numbers from 2 to 12 are 2, 3,4, 5, 6, 7, 8, 9, 10, 11 and 12 .
Prime numbers – 2, 3, 5, 7, 11
There are 11 natural numbers from 2 to 12 out of which 5 are prime numbers.
∴ Fraction of numbers that are prime is \(\frac{5}{11} .\)

Question 9.
Write the natural numbers from 102 to 113. What fraction of them are prime numbers?
Answer:
Natural numbers from 102 to 113 are 102, 103, 104, 105, 106, 107, 108, 109, 110, 111,
112 and 113
Prime numbers—103, 107, 109, 113 There are 12 natural numbers from 102 to
113 out of which 4 are prime numbers.
So, fraction of numbers that are prime is \(\frac{4}{12}=\frac{1}{3}\)

Question 10.
What fractions of these circles have X’s in them?

Answer:
There are 8 circles out of which 4 have X’s in them.
So, fraction of circles having X’s is \(\frac{4}{8}=\frac{1}{2}\)

Question 11.
Kristin received a CD player for her birthday. She bought 3 CDs and received 5 others as gifts. What fraction of her total CDs did she buy and what fraction did she receive as gifts?
Answer:
Number of CDs Kristin purchased = 3
Number of CDs she received as gifts = 5 So, total number of CDs = 8 Kristin purchased 3 CDs out of a total number of 8 CDs.
Fraction of CDs she purchased = \(\frac{3}{8}\)
Kristin received 5 CDs out of a total number of 8 CDs.
Fraction of CDs she received as gifts = \(\frac{5}{8}\)